Is there a way to bulk move objects under a collection
I can't reproduce this in 2.83 .. I can select multiple, either in the 3D View, or the Outliner, and left-drag them into the collection by releasing the left mouse-button over the appropriate line.
It may be easier, with such a large selection, in Object Mode, in the 3D View or the Outliner, to hit M. You should then be offered a dropdown menu of collections to which you may move the selection, or the option to create a new collection to move it to.